Interacting Dirac Materials

Abstract

We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in Table~\ref{Summary}, we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.

arXiv comment19 pages and 12 Figures; Contains 6 Appendices

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Cited by in corpus (7)

• Topological Phase Transitions of Dirac Magnons in Honeycomb Ferromagnets
• Dirac magnons, nodal lines, and nodal plane in elemental gadolinium
• Higher Chern numbers in multilayer ($\mathcal{N}\ge 2$) Lieb lattices: Topological transitions and quadratic band crossing lines
• GW effects on the topology of type-II Dirac cones in NiTe${}_2$, PtSe${}_2$ and PtTe${}_2$
• Bose-Einstein condensate of Dirac magnons: Pumping and collective modes
• Interacting Dirac magnons in the van der Waals ferromagnet CrBr${}_3$
• Transport of Dirac magnons driven by gauge fields